\[ x \beta = \beta_0 + \beta_1X_i + \cdots + \beta_nX_n \\ \] \[ prob = {\frac{exp(x\beta)}{1 + exp (x\beta)}} \]
\[ prob = \frac{exp( \beta_0 + \beta_1X_i + \cdots + \beta_nX_n )} {1 + exp ( \beta_0 + \beta_1X_i + \cdots + \beta_nX_n)} \]
\[ prob = \frac {1} {1 + e^{ -( \beta_0 + \beta_1X_i + \cdots + \beta_nX_n) }} \]
| Name | Piped data |
| Number of rows | 20 |
| Number of columns | 2 |
| _______________________ | |
| Column type frequency: | |
| numeric | 2 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| 학습시간 | 0 | 1 | 2.79 | 1.51 | 0.5 | 1.69 | 2.62 | 4.06 | 5.5 | ▇▇▆▅▅ |
| 입학여부 | 0 | 1 | 0.50 | 0.51 | 0.0 | 0.00 | 0.50 | 1.00 | 1.0 | ▇▁▁▁▇ |
Call: glm(formula = 입학여부 ~ 학습시간, family = "binomial",
data = lr_tbl)
Coefficients:
(Intercept) 학습시간
-4.078 1.505
Degrees of Freedom: 19 Total (i.e. Null); 18 Residual
Null Deviance: 27.73
Residual Deviance: 16.06 AIC: 20.06
최우추정량(MLE)을 찾는 것은 - 우도(Likelihood)값을 구하는 것과 동일하기 General-purpose optimization 에 함수를 정의해서 모수 초기화하여 함께 넣어 반복적으로 근사시켜 모수를 계산한다.
$$ NLL(y) = -{(p(y))} \
_{} _y {-(p(y;))} \
_{} _y p(y;) $$
fn is fn
Looking for method = Nelder-Mead
Function has 2 arguments
Analytic gradient not made available.
Analytic Hessian not made available.
Scale check -- log parameter ratio= -Inf log bounds ratio= NA
Method: Nelder-Mead
Nelder-Mead direct search function minimizer
function value for initial parameters = 13.862944
Scaled convergence tolerance is 2.06574e-07
Stepsize computed as 0.100000
BUILD 3 13.887933 13.096825
EXTENSION 5 13.862944 12.582216
EXTENSION 7 13.096825 12.067907
EXTENSION 9 12.582216 11.285614
LO-REDUCTION 11 12.067907 11.285614
LO-REDUCTION 13 11.874408 11.285614
EXTENSION 15 11.469089 10.348151
LO-REDUCTION 17 11.285614 10.348151
EXTENSION 19 10.370274 8.914547
LO-REDUCTION 21 10.348151 8.914547
EXTENSION 23 9.266657 8.226456
REFLECTION 25 8.914547 8.030679
LO-REDUCTION 27 8.259889 8.030679
LO-REDUCTION 29 8.226456 8.030679
LO-REDUCTION 31 8.114076 8.030679
HI-REDUCTION 33 8.053435 8.030679
HI-REDUCTION 35 8.052924 8.030679
LO-REDUCTION 37 8.038012 8.030679
HI-REDUCTION 39 8.033349 8.030679
LO-REDUCTION 41 8.031439 8.030144
HI-REDUCTION 43 8.030679 8.030087
HI-REDUCTION 45 8.030144 8.029950
HI-REDUCTION 47 8.030087 8.029938
HI-REDUCTION 49 8.029950 8.029917
HI-REDUCTION 51 8.029938 8.029881
LO-REDUCTION 53 8.029917 8.029881
HI-REDUCTION 55 8.029890 8.029881
LO-REDUCTION 57 8.029889 8.029880
HI-REDUCTION 59 8.029881 8.029880
HI-REDUCTION 61 8.029880 8.029879
HI-REDUCTION 63 8.029880 8.029879
REFLECTION 65 8.029879 8.029879
Exiting from Nelder Mead minimizer
67 function evaluations used
Post processing for method Nelder-Mead
Successful convergence!
Compute Hessian approximation at finish of Nelder-Mead
Compute gradient approximation at finish of Nelder-Mead
Save results from method Nelder-Mead
$par
[1] -4.076953 1.504453
$value
[1] 8.029879
$message
NULL
$convcode
[1] 0
$fevals
function
67
$gevals
gradient
NA
$nitns
[1] NA
$kkt1
[1] TRUE
$kkt2
[1] TRUE
$xtimes
user.self
0.07
Assemble the answers
method p1 p2
1 Nelder-Mead -4.076953 1.504453
glm() 함수로 구현한 것과 값이 동일한지 상호확인한다.
(Intercept) 학습시간
-4.077713 1.504645
데이터 과학자 이광춘 저작
kwangchun.lee.7@gmail.com